The decay chain \(b \to \bar{\mathrm{B}} \rightarrow \mathrm{D}^{**0} \ell^- \bar{\nu} X , \mathrm{D}^{**0}\rightarrow \mathrm{D}^{*+}\pi^-,\mathrm{D}^{*+} \to \mathrm{D}^0\pi^+, D^0 \to (\mathrm{K}\pi\; \mathrm{or} \;\mathrm{K}3\pi)\) is identified in a sample of 3.9 million hadronic Z decays collected with the OPAL detector at LEP. The branching ratio BR \((b \to \bar{B}) \times \mathrm{BR}(\bar{B} \to \mathrm{D}^0_1 \ell^-\bar{\nu} X) \times \mathrm{BR}(\mathrm{D}^0_1 \to \mathrm{D}^{*+}\pi^-)\) is measured to be \((2.64 \pm 0.79 (\mathrm{stat}) \pm 0.39 (\mathrm{syst})) \times 10^{-3}\) for the JP=1+ (D01) state. For decays into the JP=2+ (D2*0) state, an upper limit of 1.4 x 10-3 is placed on the branching ratio at the 95% confidence level.